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By Fumio Hayashi and Junko Koeda Hitotsubashi University, Japan, And EXITING FROM QE by Fumio Hayashi and Junko Koeda Hitotsubashi University, Japan, and National Bureau of Economic Research University of Tokyo February 2014 Abstract We develop a regime-switching SVAR (structural vector autoregression) in which the monetary policy regime, chosen by the central bank responding to economic conditions, is endogenous and observable. There are two regimes, one of which is QE (quantitative easing). The model can incorporate the exit condition for terminating QE. We then apply the model to Japan, a country that has accumulated, by our count, 130 months of QE as of December 2012. Our impulse response and counter-factual analyses yield two findings about QE. First, an increase in reserves raises inflation and output. Second, terminating QE can be expansionary. Keywords: quantitative easing, structural VAR, observable regimes, Taylor rule, impulse responses, Bank of Japan. We are grateful to James Hamilton, Yuzo Honda, Tatsuyoshi Okimoto, Etsuro Shioji, George Tauchen, and particularly Toni Braun for useful comments and suggestions. 1 1 Introduction and Summary Since the recent global financial crisis, central banks of major market economies have adopted quantitative easing, or QE, which is to allow reserves held by depository institutions far above the required level while keeping the policy rate very close to zero. This paper uses an SVAR (structural vector autoregression) to evaluate macroeconomic effects of QE. Reliably estimating such a time-series model is difficult because only several years have passed since the crisis. We are thus led to examine Japan, a country that has already accumulated a history of, by our count, 130 months of QE as of December 2012. Those 130 QE months come in three installments, which allows us to evaluate the effect of exiting from QE as well. Our SVAR has two monetary policy regimes: the zero-rate regime in which the policy rate is very close to zero, and the normal regime. In Section 2, we document for Japan that bank reserves are greater than required reserves (and often several times greater) when the policy rate is below 0:05% (5 basis points) per year. We say that the zero-rate regime is in place if and only if the policy rate is below this critical rate. Therefore, the regime is observable and, since reserves are substantially higher than the required level for all months under the zero-rate regime in data, the zero-rate regime and QE are synonymous. There are three spells of the zero-rate/QE regime: March 1999 - July 2000, March 2001 - June 2006, and December 2008 to date. (They are indicated by the shades in the time-series plot of the policy rate in Figure 1.) They account for the 130 months. Also documented in Section 2 is that for most of those months the BOJ (Bank of Japan) made a stated commitment of not exiting from the zero-rate regime unless inflation is above a certain threshold. That is, the exit condition in Japan is about inflation. Our SVAR model incorporates this exit condition. The model is a natural extension of the standard recursive SVAR model developed by Christiano, Eichenbaum, and Evans (1999).1 There are four variables: inflation, output (measured by the output gap), the policy rate, and excess reserves, in that order. We do not 1 Their SVAR orders variables by placing non-financial variables (such as inflation and output) first, fol- lowed by monetary policy instruments (such as the policy rate and measures of money), and financial variables (such as stock prices and long-term interest rates). 2 impose any structure on inflation and output dynamics, so the first two equations of the system are reduced-form equations. The third equation is the Taylor rule providing a shadow policy rate, while the fourth equation specifies the central bank’s supply of excess reserves under QE. We incorporate the exit condition by assuming that the central bank ends the zero-rate regime only if the shadow rate is positive (i.e., if the zero lower bound is not binding) and the inflation rate is above a certain threshold. The regime is endogenous because the regime evolution depends on inflation and output through the zero lower bound and the exit condition. In compliance with the Lucas critique, we allow the reduced-form coefficients for inflation and output to depend on the monetary policy regime. The model parameters are estimated by ML (maximum likelihood) that properly takes into account regime endogeneity. We utilize the IRs (impulse responses) and other counter-factual analyses to describe the macroeconomic effects of various monetary policies, including those of a change in the monetary policy regime. The IRs we emply are a generalization, to non-linear systems such as ours, of the standard IRs for linear systems. To describe the effect of, for example, a cut in the policy rate in the base period t, we compare the path of inflation and output projected by the model given the baseline history up to t with the path given an alternative history that differs from the baseline history only with respect to the policy rate in t. We find: • When the regime is the normal regime in both the baseline and alternative histories so that there is room for rate cuts, the IR of inflation to a policy rate cut is negative for many periods. Thus, consistent with the finding of the literature to be cited below, we observe the price 3 puzzle for Japan.2 • Under the zero-rate/QE regime, the IR of inflation and output to an increase in excess reserves is positive. This, too, is consistent with the literature’s finding. • The IR analysis can be extended by allowing the two paths to differ in more than one respect in the base period t. As an example, we set t = July 2006, the month the zero-rate/QE regime was terminated, and consider an alternative and counter-factual history of not exiting from QE in t. The two histories differ at t not just in the regime but also in the policy rate and excess reserves. We find that output and (to a less extent) inflation are lower under the alternative of extending QE to July 2006. That is, exiting from QE in July 2006 was expansionary. Turning to the relation of our paper to the literature, there is a rapidly expanding literature on the recent QE measures (called large-scale asset purchases (LSAPs)) by the U.S. Federal Reserve. Given the small sample sizes, researchers wishing to study macroeconomic effects of QE proceed in two steps, first documenting that QE lowered longer-term interest rates and then evaluating the effect of lower interest rates using macroeconomic models. In a recent review of the literature, Williams (2012) notes that there is a great deal of uncertainty surrounding the existing estimates. One reason he cites is that QE-induced interest rate declines may be atypical. Were it not for the small-sample problem, time-series analysis of QE would complement nicely those model-based analyses. There are several SVAR studies about Japan’s QE that exploit 2 In a detailed examination of the price puzzle, Braun and Shioji (2006) show that the price puzzle is pervasive for both the U.S. and Japan in the recursive SVAR model of Christiano et. al. (1999) mentioned in footnote 1. For Japan, they use monthly data from 1981 to 1996 and find that a large and persistent price puzzle arises for a variety of choices for the financial variables including commodity prices, the Yen-Dollar exchange rate, oil prices, the wholesale price index, and the 10-year yield on government bonds. They also find that the puzzle arises when each of those financial variables are placed third after inflation and output. To corroborate their finding for the U.S., we estimated the 3-variable SVAR model of Stock and Watson (2001, to be presented in Section 3) on monthly U.S. data from 1960 to 2000 and found that the price puzzle lasts for several years (Stock and Watson (2001) estimated the model on quarterly U.S. data and found that the price puzzle lasts for only a couple of quarters). For a structural model for the U.S. that generates the price puzzle, see Christiano, Eichenbaum, and Evans (2005). 4 the many QE months noted above. They can be divided into three sets: (a) those assuming the regime is observable and exogenous, (b) those with exogenous but unobservable regimes, and (c) those (like our paper) with endogenous and observable regimes. All those studies assume the block-recursive structure of Christiano, et. al. (1999) mentioned in footnote 1. Honda et. al. (2007) and Kimura and Nakajima (2013) fall in category (a). Using Japanese monthly data covering only the zero-rate period of 2001 through 2006 and based on SVARs that exclude the policy rate (because it is zero), Honda et. al. (2007) find that the IR of inflation and output to an increase in reserves is positive. Kimura and Nakajima (2013) use quarterly data from 1981 and assume two spells of the QE regime (2001:Q1 - 2006:Q1 and 2010:Q1 on). They too find the expansionary effect of excess reserves under QE.3 Falling in category (b) are Fujiwara (2006) and Inoue and Okimoto (2008).4 Both papers apply the hidden-stage Markov switching SVAR model to Japanese monthly data. They find that the probability of the second state was very high in most of the months since the late 1990s. For those months, the IR of output to an increase in base money is positive and persistent. The regime in Iwata and Wu (2006) and Iwata (2010), in contrast, is necessarily endogenous because the policy rate in their VAR, being subject to the zero lower bound, is a censored variable.
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